```Date: Feb 11, 2013 4:19 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <59abfe03-8386-4d06-8f54-acfbf19a50d0@x15g2000vbj.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 11 Feb., 16:40, William Hughes <wpihug...@gmail.com> wrote:> > On Feb 11, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > On 11 Feb., 11:55, William Hughes <wpihug...@gmail.com> wrote:> >> > > > On Feb 11, 8:50 am, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > > > There exists a natural number m such that d is line number m is false.> >> > > Yes so, alas not quite correct if d is assumed to "exist".> >> > > If d is assumed to exist, we have> >> > > 1) We cannot *find* a natural number m such that d is the m-th line of> > > the list.> >> > According to you> >> >    if L is a potentially infinite list, and d is> >    the potentially infinite diagonal> >> >    if for every natural number n, d is not the nth> >    line of L  then> >> >    *There does not exist* a natural number m such that> >    d is the mth line of L> >> > Do you wish to withdraw this claim?> > No. This claim is obviously correct.> > Only *if the complete existence of the not completely existing> diagonal d is assumed*, it would be necessary to have it in the list> and (since every line of the list contains everything that is> contained by its predecessors) to have it in a line of the list. But> obviously a potentially infinite diagonal does not exist completely> (as the potentially infinite list does not exist completely).> > So why should anything be withdrawn?The notion of potential infiniteness should be withdrawn as it is incompatible with the notion of "set".One cannot have a set whose membership is only potentially determined.In all standard set theories there is a set which contains {} as a member and which for each of its members, m, also contains (m union {m}).Since this is apparently not the case in WMytheology , then no set theory in WMytheology is compatible with standard mathematics , and thus WMytheology irreleveant to standard mathematics.--
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